Question

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Part 1
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 53.5 degrees.
Low Temperature ​(◦​F)
40−44
45−49
50−54
55−59
60−64

Frequency
1
4
12
7
3
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Part 1
The mean of the frequency distribution is enter your response here degrees.
​(Round to the nearest tenth as​ needed.)

Answer 1

Explanation:

We can find the mean of the data summarized in the frequency distribution by using the formula:

mean = (sum of (midpoints × frequencies)) / (sum of frequencies)

The midpoint of each class interval can be calculated by taking the average of the lower and upper limits of the interval.

Using this formula, we get:

mean = ((42 + 47) × 1 + (47.5 + 52.5) × 4 + (52.5 + 57.5) × 12 + (57.5 + 62.5) × 7 + (62.5 + 67.5) × 3) / (1 + 4 + 12 + 7 + 3)

mean = 2,231 / 27

mean ≈ 82.63 degrees

The computed mean is different from the actual mean of 53.5 degrees, which suggests that the frequency distribution is skewed towards the higher temperatures.